"Tomorrow is an opportunity for the leaders of the UK, France and Germany to come together... and make very clear to president Putin that we need this ceasefire to hold, to be a lasting one and to open the way for a real political transition," Cameron's spokeswoman told reporters on Thursday.
The truce that came into force at midnight on Friday and was negotiated by the US and Russia is the first major cessation of hostilities in the five-year war in Syria that has claimed more than 270,000 lives.
The call will be the first time the leaders have spoken since it came into effect.
Russia, a key ally of the regime of President Bashar al-Assad, has said it will carry on striking "terrorist groups" but non-jihadist Syrian rebels say Moscow has kept on bombarding other targets as well.
Cameron's spokeswoman described the truce as "fragile".
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She said the call was about "wanting to make sure that the Russians fully support what they signed up to in the UN Security Council resolution at the end of last year to work towards peace in Syria".
Peace talks which aim to end the conflict are due to resume in Geneva on March 9. An earlier round was cut short amid intensifying Russian air strikes in Syria.
Speaking in parliament on Wednesday, Cameron said the ceasefire was "imperfect" but called it "an important step forward".
"Not every group is included in the ceasefire, but basically we are not seeing the attacks that were taking place on the moderate opposition, which is welcome," Cameron said.
"It has also enabled us, with others, to get aid to communities that desperately need it, including through air drops and convoys.
"I would not put too much optimism into the mix right now, but this is progress and we should work on it."